Algebra History

Overview

Mostly based on the Rhind papyrus written at about 1650B.C. Can solve problems with one unknown now called the “method of false position” Rhetorical-problems are stated and solved verbally Can solve some problems with two unknowns. However, the Egyptian Algebra was slowed down by their troublesome unit fractions 1.Egyptian Algebra Mostly based on the Rhind papyrus written at about 1650B.C. Can solve problems with one unknown now called the “method of false position” Rhetorical-problems are stated and solved verbally Can solve some problems with two unknowns. However, the Egyptian Algebra was slowed down by their troublesome unit fractions a+7=30 a=30-7 =23 2.Babylonian Algebra 1800 - 1600 B.C. More advanced than Egypt had a general procedure similar to solving quadratic equations dealt with the equivalent of two equations in two unknowns considered some problems which involve more than two unknowns Also consider equations of higher degree. Some symbols but still rhetorical Taught through examples( no reasons given) 3.Greek Geometrical Algebra Represent quantities as geometrical magnitudes In content only slightly beyond the Babylonians but little practical value as it was in geometrical form This approach had also slowed down the progress in Algebra for several centuries

6.Arabic Algebra improved the Hindu number symbols worked freely with irrationals Unlike the Hindu, they rejected negative numbers The word “Algebra” comes from Arab textbook entirely rhetorical 4.Diophantine Algebra Ended the Geometrical Algebra introduced the syncopated style of writing equations but still rhetorical 5.Hindu Algebra took zero as a number and discussed operations and involve this number introduced negative numbers to represent debts developed correct procedures for operating with irrational numbers. Again, only examples, no reasons or proof 7.European Algebra after 1500 Negative numbers were known but not fully accepted mostly rhetorical made many important improvements in symbolism Symbolic algebra started at only 1637 By end of 17 century, symbolism was used deliberately (previously was just accidental) 8.Modern Algebra scope of algebra was expanded to the its form and structure and not limited to ordinary systems of numbers developed non-commutative algebras demonstrated that complex numbers could be expressed as a formal algebra

Algebra Long long ago, the world developed 7 forms of algebra (Egyptian, Babylonian, Greek Geometrical, Diophantine, Hindu, Arabic and European algebra) Greek Geometrical Algebra invented during classical period Avoided irrational numbers Geometrical magnitudes Egyptian Algebra Based on Rhind Papyrus Method of false position Mainly rhetorical-stated and solved verbally Babylonian Algebra High developed algebra Dealt with equivalent of systems Right now we combined all the different algebra and improve a little to create… Abstract Algebra Used now all over the world Summary

CREDITS Heng Teng Hiang Lee Wen Sin jAnice Soo Mona Tan Class: Mo7102 Finalized on:20/3/07